Mean-field theory for heterogeneous random growth with redistribution
Abstract
We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong enough to prevent localization, i.e., extreme concentration on the fastest growing site. In the presence of an additional temporal noise in the growth rates, a third partially localized phase is predicted theoretically, using results from Derrida's random energy model. Such temporal fluctuations mitigate concentration effects, but do not make them disappear. We discuss our results in the context of population growth and wealth inequalities.
Fields of Study & Subjects
Complex Systems and Time Series Analysis
Ecosystem dynamics and resilience
Theoretical and Computational Physics
Publication details
- Journal / source
- Physical review. E
- Publisher
- American Physical Society (APS)
- Volume
- 113
- Issue
- 3
- Pages
- L032101–L032101
- Publication date
- 12 February 2026
- Language
- EN